Inequalities concerning the \(L^p\)-norm of a polynomial
type: Item
instance of: scholarly article
title: Inequalities concerning the \(L^p\)-norm of a polynomial
zbMATH Open document ID: 1010.41005
author: Aijaz Ahmad Bhat
author: Mohammad Sayeed Pukhta
author: K. K. Dewan
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-11-29T00:00:00Z
review text: Let \(K\geq 1\), \(\mu\geq 1\) and let \(p(z)=a_0+a_\mu z^\mu+\cdots+a_nz= ^n\) be a complex polynomial of degree \(n\) not vanishing in the disk \(|z|<K\). The authors show that for \(q\geq 1\) one has \(||p'||_q\leq c||p||_q,\) where \(||\cdot||_q\) denotes the \(L_p\) norm on \(|z|=1\) and \(c\) is an explicitly given constant, which depends on \(n\), \(\mu\), \(K\), \(p(0)\) and the coefficient \(a_\mu\) of \(f\). This generalizes a result of de Bruijn who considered the case \(K=\mu=1\).
Mathematics Subject Classification ID: 41A17
Mathematics Subject Classification ID: 30C10
zbMATH DE Number: 1215751
zbMATH Keywords: \(L^p\) norm
zbMATH Keywords: complex polynomials
zbMATH Keywords: derivative
zbMATH Keywords: inequalities
zbMATH Keywords: extremal problems
reviewed by: Władysław Narkiewicz
MaRDI profile type: Publication
full work available at URL: jmaa.1998.5980
OpenAlex ID: W2042104146
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DOI: 10.1006/JMAA.1998.5980
description: scientific article; zbMATH DE number 1215751